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Hypergeometric Functions
HypergeometricPFQ[{a1,a2,a3},{b1,b2},z]
Specific values
For integer and half-integer parameters and fixed z
For fixed z and a1=-1/2, a2>=-1/2
For fixed z and a1=-1/2, a2=4, a3>=4
For fixed z and a1=-1/2, a2=4, a3=4
For fixed z and a1=-1/2, a2=4, a3=4, b1=-7/2
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http://functions.wolfram.com/07.27.03.am4r.01
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HypergeometricPFQ[{-(1/2), 4, 4}, {-(7/2), -(3/2)}, -z] ==
(1/(5376 (1 + z)^12)) (5376 + 72704 z + 412160 z^2 + 248832 z^3 -
50177280 z^4 + 698134614 z^5 - 1159846749 z^6 + 410395840 z^7 -
24016652 z^8) + (2145 (4290 z^(9/2) - 21515 z^(11/2) + 21150 z^(13/2) -
4872 z^(15/2) + 176 z^(17/2)) ArcSinh[Sqrt[z]])/
(256 Sqrt[1 + z] (1 + 12 z + 66 z^2 + 220 z^3 + 495 z^4 + 792 z^5 +
924 z^6 + 792 z^7 + 495 z^8 + 220 z^9 + 66 z^10 + 12 z^11 + z^12))
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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